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When the Labor Department reported in February that average hourly earnings had jumped 2.9 percent in January, it looked as if the long, steady recovery in the U.S. job market might at last be translating into faster wage gains for the nation’s workers.

Then came Friday and the latest jobs report, which showed that wage growth was weaker in January than initially reported and that the gains in February were weaker still, up just 2.6 percent from a year earlier.

The muddled data on wages was a potent reminder that even the strongest job market in a generation has not been robust enough to reverse a long-standing pattern of lagging pay.

But the mixed messages also highlight the challenge of trying to figure out where wages are headed: Not only are the sources of the data volatile, but economists say they may also be declining in quality.

In recent months, different sources have told sharply diverging stories about how quickly companies are raising employees’ pay. Wage growth may be slowing drastically after a period of strong gains, or it may be picking up after an extended slump. Or it may be stuck at more or less the same plodding pace that workers have become accustomed to for much of the economic recovery.

“We have trouble measuring any of these things,” said Tara Sinclair, an economist at George Washington University and for the job-search site Indeed. “This is definitely one of those situations where you can feed in the data and get out whatever response you’re looking for.”

The problem is not new. It has, however, risen in importance as wage growth — why it has been slow, and when that might change — has emerged as a pre-eminent issue in Washington and on Wall Street. Congressional Republicans, their eyes on the fall elections, are seeking evidence that their recently passed tax cuts are making an impact on paychecks. Federal Reserve policymakers are looking for signs that the tightening labor market is causing inflation.

Financial markets tumbled a month ago after the data showing strong wage gains heightened fears that inflation would pick up, forcing the Fed to hasten interest-rate increases. The report released Friday had the opposite effect: Stocks rallied on the prospect that strong job growth could continue without causing the economy to overheat.

Robin Brooks, chief economist for the Institute of International Finance, an industry group, said the market volatility over wages a month ago was “way premature.”

All economic figures come with significant uncertainty. It is common for different measures to disagree about the pace of job growth, consumer spending and other key indicators. But wages pose a particular measurement challenge. Surveys, the source of much economic data, can be unreliable because people often err in recalling the details of their income, or they may decline to answer questions about it. Companies, for their part, track how much they pay their employees but not necessarily how many hours they work, at least for those who are salaried.

The measure that tends to get the most attention from investors and the media is average hourly earnings, a figure released by the Bureau of Labor Statistics as part of each month’s jobs report. The figure, based on a survey of employers, is timely and easily understood: simply the total amount that companies paid workers in a given period, divided by the hours those employees worked.

Despite the familiarity of the average hourly earnings figure, however, economists say that it is among the least reliable indicators, especially in the short run. The monthly data is prone to distortions because of bad weather or quirks of the calendar (even an oddly timed holiday can skew the numbers). The measure is also affected by trends like the retirement of the baby boom generation, rising health care costs and the spread of contract work — long-run shifts that affect average earnings in subtle but significant ways.

Other measures try to account for at least some of these issues by, for example, factoring in the cost of benefits or by controlling for the changing mix of industries in the U.S. economy. But these indicators have their own problems, including smaller sample sizes. And almost all are released at a significant delay.

“The problem is that there is no perfect measure of wage growth,” said Ian Shepherdson, chief economist at Pantheon Macroeconomics, a research firm. “There is no right answer; there never will be a right answer.”

The best way to deal with the conflicting signals, economists say, is to look at a range of indicators — or to average them together — and to ignore short-term fluctuations in favor of longer-term trends. Taken together, the various measures suggest that wage growth has been weak but has crept upward gradually as the economy has improved.

Focusing on the long run, however, does not solve another problem that increasingly concerns economists: signs that data about Americans’ earnings and income is getting less reliable. Most government statistics, for instance, have failed to adapt to the rise of the so-called gig economy and other trends that are changing the relationship between companies and workers. The hourly earnings measure in the monthly jobs report excludes Uber drivers and similar contractors.

“I don’t think any of these measures do very well with nonstandard work arrangements,” said Katharine Abraham, a University of Maryland economist who recently led a government commission that studied how data might inform public policy.

Moreover, Americans are increasingly refusing to respond to government surveys. The response rate to the monthly Current Population Survey, the data source that underlies the unemployment rate and many other key statistics, has eroded in recent years. Of the households that do respond, about a third refuse to provide information about their earnings, a rate much higher than for most other questions. Similar problems have affected other government and private-sector surveys.

“Every measure of data quality that we look at seems to have declined over time,” said Bruce D. Meyer, a University of Chicago economist who has studied falling response rates.

Economists who have studied the issue say that aggregate statistics, like the overall median hourly wage, remain reliable. But falling response rates are a bigger problem when it comes to studying high or low earners, or specific demographic groups. And the shrinking sample sizes make it harder to distinguish between true patterns and statistical noise.

Government statisticians are trying to find ways to improve the data, perhaps by supplementing surveys with records from Social Security records, tax filings or other sources. But such records pose logistical and potentially legal hurdles, and often are not available on a monthly or even quarterly basis.

The private sector, too, is looking for solutions. The payroll processing firm ADP recently began releasing a quarterly report on earnings based on data it collects from 330,000 U.S. employers.

“To really get down to the details with surveys is hard,” said Ahu Yildirmaz, who heads the ADP research group that produces the report. “This is where the private data comes into the picture.”

Independent economists said that data from private sources like ADP showed promise, but could not replace government statistics. And because they are relatively new, it is not clear how they will respond when a recession hits or the economy changes in other ways.